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Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative
Joint Authors
Aguilar, José Francisco Gómez
Hernández, Margarita Miranda
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-20
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented.
The order of the derivative is considered as 0 < β , γ ≤ 1 for the space and time domain, respectively.
The fractional derivative of Caputo type is considered.
In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case.
In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form.
In order that the equation preserves the physical units of the system two auxiliary parameters σ x and σ t are introduced characterizing the existence of fractional space and time components, respectively.
A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ .
The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.
American Psychological Association (APA)
Aguilar, José Francisco Gómez& Hernández, Margarita Miranda. 2014. Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1013633
Modern Language Association (MLA)
Aguilar, José Francisco Gómez& Hernández, Margarita Miranda. Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative. Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1013633
American Medical Association (AMA)
Aguilar, José Francisco Gómez& Hernández, Margarita Miranda. Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1013633
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013633